Euler's Method Tutorial a method of solving ordinary differential equations using Microsoft Excel Introduction

Fig 6 - the completed function and ...

Fig 7 - the result

    Now that we have entered this function, and it is working in the background, it produces a number.  Check to see that this number

is ok, it should appear as in Fig 7.  If you ever forget whether -0.5 is numeric data or data produced by a function, just click on the

cell and the function will appear in the special cell again.

    Ok, now we have filled in completely the t=0 line, so it's time to move on, literally.  We first need to define the next time interval. 

Do this by entering a formula for the time t=1.  Add the value of 

Dt to the value of t in the cell directly above it.  Don't just type in

the number .001, but instead reference the cell where 

Dt is located, that way if you want to change Dt later on all you'll have to do is

change one cell and all the rest will automatically update themselves.  Don't forget to make it an absolute reference!  When you are

done, your equation should look like:  =A4+$F$5  The value of .001 should appear in the cell as expected.

    Now, finally, we get to put old Euler to work:  If you don't remember how to get the next value of the position in time, refresh

your memory by looking back above.  The equation you enter into the B5 cell should look like:  =B4+C4*(A5-A4)  Why?  Next,

using the same approximation, move on to the B6 cell and enter the correct equation for the value of the velocity.  The answer it

produces when you hit the enter key should be -.05  Now for the last cell in the time step t=1.  Since we have already typed in the

formula which relates the acceleration to the position of the pendulum at any instant, all that we need do is copy the equation from

the t=0 cell to the t=1 cell.  Do this by first highlighting the D4 cell and the D5 cell simultaneously (ie:  hold down the button while

moving the mouse over both of them)  Then either click on the Edit->Paste Down menu or just type in Control-D and the formula

will automatically copy itself into the D5 cell.  Compare the two equations in the D4 and D5 cell.  Why did some of the numbers

change, and some did not?